Calculate the electric field (in full vector form) at the center of a half ring of charge of radius R and inear charge density, A that lies in the x – y plane with the center of the ring located at the origin. The harge covers the polar angle range 1/2 < 0 < 37/2. See the diagram below. R (ou may save yourself some time or algebra in the calculation if you think about the geometry of the rrangement before you start calculating.

We have calculated the electric field due to a uniformly charged disk of radius R, along its axis. Note that the final result does not contain the integration variable r: R. Q/A 2€0 Edisk (x² +R*)* Edisk perpendicular to the center of the disk Uniform Q over area A (A=RR²) Show that at a perpendicular distance R from the center of a uniformly negatively charged disk of CA and is directed toward the disk: Q/A radius R, the electric field is 0.3- 2€0 4.4.1b

Assume a uniformly charged ring of radius R and charge Q produces an electric field E at a point Pon its axis, at distance x away from the center of the ring as in Figure a. Now the same charge Q is spread uniformly over the circular area the ring encloses, forming a flat disk of charge with the same radius as in Figure a. How does the field Eick produced by the disk at P compare with the field produced by the ring at the same point? O O Ek Ering O impossible to determine

Another special case turns out to be of considerable interest. Let's see what the electric field is like near the center of a uniformly charged disk (x small, but not zero, for the reasons just given). Suppose that we are so close to the disk that x is very small (x > x). QIA Show that near the disk E- R